Aptitude - True Discount - Discussion

As simple as that, Frist man buy and sell a cow on the same day. And he buys bow on credit 3000 for 2year on 10% interest.

So he has to pay after two years. (3000*2*10) /100=600 as interest. Total is 3600.
And he sold the cow the same day in 3600 rs.
So, at the end he did not get any profit. i.e Zero gain.

@All.

Here let's assume that I am selling the cow to you.
So, here I purchased with 3000. So to get any profit I need to sold it to you more than 3000.

Here you agree to pay 10% interest rate per annum for 2 years.

So, When I calculate with that interest, after 2 years my cow will cost 3600. And you pay exactly 3600.

So profit is 0 for me.

Hope this is clear explanation.

@ Shalini Negi. The buyer here is referred to the first person, the one who bought the cow for 3000. The buyer pays the money in installments. So the interest is also to be paid. Since nothing is mentioned we go with simple interest.

The buyer receives a profit of 600 (3600-3000) on the first day.

He pays the interest for 2 years which is equal to 3000*2*10% = Rs. 600.

Hence at the end of 2 years, he receives no profit i.e., 600-600 = Rs. 0.

The formula used is.

True discount = {Banker's discount x 100}/{100+ (rate x time)}.

Let us assume,
(P. W) 2 = present worth in second case.
P. A = Payable amount
T. D = True Discount
P. A = (P. W) 2 + T. D.
3600 = (P.W)2 + 600.

=>(P. W)2 = 3600 - 600 = 3000
Gain = (P.W)2-PW = 3000 - 3000 = 0,
%gain= (0/3000) * 100 = 0%.
So, the Answer will be 0%.

What do you mean bu credit " allowing the buyer a credit of 2 years"? Please explain me.

Value of cow is Rs.3000
Now
100----->10
3000---->?

3000*10
------------ =300
100

Now credit 2 years,
so, 300*2=600,
3000+600=3600,
3600=3600,
So 0 discount.

Guys, see no formula required for this question.

C.P = 3000, S.P = 3600.

Now if seller will deposit 3000 in bank, after 2 years his profit will be 600. Because interest is 10% per annum, so for 2 years it will be 20%. 20% of 3000 is 600. So value of 3000 in future will be same as value of 3600 in future.

See this question is a tricky one in its language pattern. Here its written "A man purchased a cow for 3000 and sold it the same day for 3600 " now this very statement means that the man has sold the cow instantly for 3600 rupees while making a gain of net 600 rupees. And please Note the word "Purchased" because this is the key word. Purchase means buying any thing legaly like for some agreement of emi etc in which some money is given first and remaining later on. Whereas Buy means to buy things directly without any future payment to be done.

So now here as you can see that there is only one Man being talked about, so this man Purchased the cow for 3000 on an interest rate of 10% annum for a time period of 2 year hence the man has to pay an interest of 3000*2*10/100= 600 rupees, and as you know that Man had already made a gain of 600 rupees by selling the cow for 3600 rupees, which mean that no profit actually.

And one more thing, you can also interpret this question like this. To sell a product the word Selling is only used, whereas for taking that product there are two ways, either you buy it by paying full amount, or you can purchase that product with any kind of agreement that the shopkeeper is giving like discount, installment scheme etc.

3000 's -> 10% = 300.

2year credit =300 * 2 = 600.
3600 - 600 = 3000(same to cost prize).
So, 0%profit.